Overview
- Group
- SmallGroup(1440,5685)
- Rank
- 5
- Schläfli Type
- {4,30,2,3}
- Vertices, edges, …
- 4, 60, 30, 3, 3
- Order of s0s1s2s3s4
- 60
- Order of s0s1s2s3s4s3s2s1
- 2
- Also known as
- if this polytope has a name.
Special Properties
- Degenerate
- Universal
- Orientable
- Flat
Quotients maximal quotients in bold
2-fold
3-fold
4-fold
5-fold
6-fold
10-fold
12-fold
15-fold
20-fold
30-fold
Covers minimal covers in bold
None in this atlas.
Representations
Permutation Representation (GAP)
s0 := (31,46)(32,47)(33,48)(34,49)(35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)(44,59)(45,60);; s1 := ( 1,31)( 2,35)( 3,34)( 4,33)( 5,32)( 6,41)( 7,45)( 8,44)( 9,43)(10,42)(11,36)(12,40)(13,39)(14,38)(15,37)(16,46)(17,50)(18,49)(19,48)(20,47)(21,56)(22,60)(23,59)(24,58)(25,57)(26,51)(27,55)(28,54)(29,53)(30,52);; s2 := ( 1, 7)( 2, 6)( 3,10)( 4, 9)( 5, 8)(11,12)(13,15)(16,22)(17,21)(18,25)(19,24)(20,23)(26,27)(28,30)(31,37)(32,36)(33,40)(34,39)(35,38)(41,42)(43,45)(46,52)(47,51)(48,55)(49,54)(50,53)(56,57)(58,60);; s3 := (62,63);; s4 := (61,62);; poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP)
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(63)!(31,46)(32,47)(33,48)(34,49)(35,50)(36,51)(37,52)(38,53)(39,54)(40,55)(41,56)(42,57)(43,58)(44,59)(45,60); s1 := Sym(63)!( 1,31)( 2,35)( 3,34)( 4,33)( 5,32)( 6,41)( 7,45)( 8,44)( 9,43)(10,42)(11,36)(12,40)(13,39)(14,38)(15,37)(16,46)(17,50)(18,49)(19,48)(20,47)(21,56)(22,60)(23,59)(24,58)(25,57)(26,51)(27,55)(28,54)(29,53)(30,52); s2 := Sym(63)!( 1, 7)( 2, 6)( 3,10)( 4, 9)( 5, 8)(11,12)(13,15)(16,22)(17,21)(18,25)(19,24)(20,23)(26,27)(28,30)(31,37)(32,36)(33,40)(34,39)(35,38)(41,42)(43,45)(46,52)(47,51)(48,55)(49,54)(50,53)(56,57)(58,60); s3 := Sym(63)!(62,63); s4 := Sym(63)!(61,62); poly := sub<Sym(63)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma)
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;